Let A be a complex unital Banach algebra, let be an element in it and let 0 < ϵ < 1.. In this article, we study the upper and lower hemicontinuity and joint continuity of the condition spectrum and its level set maps in appropriate settings. We emphasize that the empty interior of the -level set of a condition spectrum at a given plays a pivotal role in the continuity of the required maps at that point. Further, uniform continuity of the condition spectrum map is obtained in the domain of normal matrices. © 2019 Australian Mathematical Publishing Association Inc.